Rewrite as a simplified fraction. ${0.1\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 13.3333...\\ 10x &= 1.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 12}$ ${x = \dfrac{12}{90}} $ ${x = \dfrac{2}{15}} $